THE USE OF REFERENCE OBJECTIVES IN MULTI OBJECTIVE OPTIMIZATION

THE USE OF REFERENCE OBJECTIVES IN MULTI OBJECTIVE OPTIMIZATION

1980 | Andrzej P. Wierzbicki
The paper presents a survey of known results and some new developments in the use of reference objectives in multiobjective optimization. Reference objectives are any reasonable or desirable point in the objective space and can replace weighting coefficients or utility functions. The main conclusions are: any point in the objective space, whether attainable or not, can be used to derive scalarizing functions with minima at Pareto points. The entire basic theory of multiobjective optimization, including necessary and sufficient conditions of optimality and existence of Pareto-optimal solutions, can be developed using reference objectives. Reference objectives are practical for solving problems such as testing Pareto-optimality, scanning the set of Pareto-optimal solutions, interactive solving of multi-objective problems, group assessment of solutions, and solving dynamic multiobjective optimization problems. The paper aims to reevaluate basic assumptions in multicriteria optimization from a pragmatic perspective. It addresses why known methods in multicriteria analysis are not fully operational in applications. It questions whether individuals really maximize utility functions in decisions or instead aim to attain certain goals or aspiration levels. It suggests reexamining the basic axioms of multicriteria analysis. Pareto formulated the foundations of multicriteria optimization in 1896, using preference relations and weighting coefficients. Weighting coefficients play a central role in the contemporary paradigm of multicriteria analysis. In economic theory, consumers are assumed to maximize utility functions, which correspond to Pareto weighting coefficients. This has been confirmed by empirical studies and axiomatic foundations of preference orderings and utility theory. However, economic theory deals with averages of thousands of decisions, not single decisions. While consumers on average behave as if maximizing an aggregated utility function, no individual does so. Reference objectives, such as lists of items to buy or standards for a house, are usually determined partly subconsciously. While the average of such actions can be described by maximizing a utility function, utility theory does not describe how a single decision is made.The paper presents a survey of known results and some new developments in the use of reference objectives in multiobjective optimization. Reference objectives are any reasonable or desirable point in the objective space and can replace weighting coefficients or utility functions. The main conclusions are: any point in the objective space, whether attainable or not, can be used to derive scalarizing functions with minima at Pareto points. The entire basic theory of multiobjective optimization, including necessary and sufficient conditions of optimality and existence of Pareto-optimal solutions, can be developed using reference objectives. Reference objectives are practical for solving problems such as testing Pareto-optimality, scanning the set of Pareto-optimal solutions, interactive solving of multi-objective problems, group assessment of solutions, and solving dynamic multiobjective optimization problems. The paper aims to reevaluate basic assumptions in multicriteria optimization from a pragmatic perspective. It addresses why known methods in multicriteria analysis are not fully operational in applications. It questions whether individuals really maximize utility functions in decisions or instead aim to attain certain goals or aspiration levels. It suggests reexamining the basic axioms of multicriteria analysis. Pareto formulated the foundations of multicriteria optimization in 1896, using preference relations and weighting coefficients. Weighting coefficients play a central role in the contemporary paradigm of multicriteria analysis. In economic theory, consumers are assumed to maximize utility functions, which correspond to Pareto weighting coefficients. This has been confirmed by empirical studies and axiomatic foundations of preference orderings and utility theory. However, economic theory deals with averages of thousands of decisions, not single decisions. While consumers on average behave as if maximizing an aggregated utility function, no individual does so. Reference objectives, such as lists of items to buy or standards for a house, are usually determined partly subconsciously. While the average of such actions can be described by maximizing a utility function, utility theory does not describe how a single decision is made.
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